You can try using Value instead of ComponentToCompare. If you use ComponentToCompare it has to have a value. Try setting Value to ${DateDeleted} or however the other property is called.
Do you means, I have to set a new property to my field value (DateDeleted) and (DateSubmitted), and after that set these property into CompareValidator value?
Yes, you need to data-bind the Value of the required DatePicker to a new page property. And set Value of the CompareValidator as instructed in my previous reply and not ${DateDeleted > DateSubmitted}. The Value property of the CompareValidator is the Value you want to compare to. ComponentToCompare should not be set in this case.